MacBook - Macbook thinks charger is plugged in...

Hi, here recently i noticed the brightness of my macbook fluctuating...wasn't sure wat was causing it until i noticed that when this happened, the battery symbol in my menu bar would show either the charging or charged symbol...i'm taking this to mean that the macbook thinks the Magsafe is plugged in...any ideas on how to fix this, or anyone else having this problem?...it's not affecting my work, to my knowledge...but it's very aggravating...any help would be appreciated...Thanks!...

There is a known issue with the screen flickering on certain MacBooks, so it may be just a coincidence that the two problems are occurring at the same time.

The first thing I would do is to check the magsafe port on the side of the MacBook and make sure it's clean and clear of debris. It's not unusual for the connector to attract bits of debris. Secondly, I'd reset the PMU, following this procedure: